Optical frequency combs

The optical frequency chains discussed in the previous section are difficult to build. Many lasers and optical harmonic generators have to be phase-locked and frequency-stabilized, and the whole setup can easily fill a large laboratory. Furthermore, each of these chains is restricted to a single optical frequency, which is linked to the cesium clock, just like the present frequency standard. 

Recently, a new technique has been developed [1323] that allows the direct comparison of widely different reference frequencies and thus considerably simplifies the frequency chain from the cesium clock to optical frequencies by reducing it to a single step. Its basic principle can be understood as follows (Fig. 9.91) The frequency spectrum of a mode-locked continuous laser emitting a regular train of short pulses with repetition rate 1/AT consists of a comb of equally spaced frequency components (the modes of the laser resonator). The spectral width Aw = 2jt/T of this comb spectrum depends on the temporal width T/Ar of the laser pulses (Fourier theorem). Using femtosecond pulses from a Tusapphire Kerr lens mode-locked laser, the comb spectrum extends over more than 30 THz. 

The electric field of the femtosecond pulses is shown in Fig. 9.87. If there were no phase shifts, each pulse would be an exact replica of the previous pulse, i.e. E(t) = E(t — T). However, due to intracavity dispersion in the laser resonator, the group velocity and the phase velocity may be different. This causes a phase shift A = T wcE of the peak of the carrier wave E(t) with respect to the peak of the pulse envelope. 

The Fourier transformation of E t) gives the frequency spectrum ( ), shown in the lower part of Fig. 9.87. 

The spectral width Aty can be further increased by focusing the laser pulses into a special optical fiber, which consists of a photonic crystal (Fig. 9.88) where by self-phase modulation the spectrum is considerably broadened and extends over one decade (e.g., from 1064 nm to 532 nm) (Fig. 9.89). This corresponds to a frequency span of 300 THz [1327] It was found by interference experiments, that the coherence properties were preserved in this broadened spectmm, i.e. the nonlinear processes in the optical fiber did not destroy the coherence of the original frequency comb. 

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The enormous difficulty of making optical frequency measurements has been a major obstacle to progress. The optical frequency comb generator devised by Hansch overcomes these difficulties, and promises to revolutionize spectroscopy. The technique, based upon a mode-locked laser, makes it possible to connect microwave and optical frequencies, or to determine relative optical frequencies [20,21], In particular, it allows to transport the stability of optical transitions into the microwave frequency range. A report by J. Hall about these developments can be found in these proceedings. 

Despite all of the above-mentioned limitations in accuracy of optical interferometry, it is still widely used in the determination of the wave-numbers of atomic transitions, since optical frequency metrology (synthesis chains, optical frequency combs, etc, 4) does not yet have the wide spectral coverage provided by the broad-band interferometers. As an example, a recent absolute wave-number determination of the Cs D2 resonance line at 852 nm is with a Fabry-Perot interferometer, saturated absorption and a grating-eavity semiconductor laser [76]. These results are of interest to various Cs atomic fountain measurements and lead to better determinations of fundamental constants, such as h/mp and a, [77] as well as of the acceleration due to gravity, g [78,79]. 

Thorpe, M. J., Balslev-Clausen, D., Kirchner, M. S. and Ye, J. (2008) Cavity-enhanced optical frequency comb spectroscopy application to human breath analysis . Optics Express, 16(4), 2387-2397. 

All the projects benefit hugely from the successful development in the frequency measurements techniques thanks to the optical frequency comb technique [48],... 

Thorpe, M.J. Hudson D.D. Moll, K.D. Lasri, J. Ye, J. Cavity-ringdown molecular spectroscopy based on an optical frequency comb at 1.45-1.65 tm. Optic. Lett. 2007,... 

Even higher precision can be reached with the optical frequency comb (see Sect. 9.7). 

A simplified picture for comparing the frequency [Pg.571]

The experimental realization is based on the comparison of the optical frequency comb with the Cs-atomic clock, which represents up to date the frequency standard. A dye laser at X = 486 nm is stabilized to a frequency vi which differs from the frequency Vc of one of the teeth of the optical frequency comb by the radiofrequency /i. The output of the dye laser is frequency doubled in a BBO-crystal and is then sent collinearly to the H-atom beam into an enhancement cavity, where it excites the two-photon transition 15 -> 25 of the H-atom [1326]. The radio-frequency... 

A possible direct link between the UV frequency of the two-photon 15 25 transition in the H atom and the Cs clock in the microwave range with the optical frequency comb is illustrated in Fig. 9.91. 

The optical frequency comb allows a very accurate determination of the Rydberg constant from measurements of the absolute frequency of the 15 25 transition in the hydrogen atom (see also Sect. 2.5.4). 

A user friendly version of optical frequency combs has been realized with fibre lasers [1328]. Mode-locked fibre lasers doped with Er of Yb ions have only a few adjustable optical components which make them easy to handle and facilitates their maintenance. Meanwhile optical frequency combs are commercially available. 

The spectral range of the optical frequency comb can be extended into the infrared and the ultraviolet region down into the vacuum ultraviolet (VUV) and even into the soft X-ray region (XUV). The experimental realization is shown in Fig. 9.92a. 

The optical frequency comb (for which Th.W. Hansch and J. Hall received the Nobel Prize) has meanwhile found numerous applieations, as for instance the very aecu-rate measurement of optical frequencies, whieh has been discussed in the previous section. It is much simpler than former techniques but reaches an accuraey that is two to three orders of magnitude higher. 

Molecular Spectroscopy with Optical Frequency Combs... 

At first we will discuss the use of a single optical frequency comb where the probe is placed inside an optical resonator with resonance frequencies matching the modes of the comb. Therefore all absorption frequencies of the molecule under investigation contribute simultaneously to the absorption of the comb. Outside the resonator a prism or grating disperses the different frequencies and a CCD array can detect simultaneously all absorption lines inside the spectral range A v of the comb. For a measuring time Af the signal-to-noise ratio is increased by a factor VAr Av. 

Assume that the comb separation Av = 100 MHz of an optical frequency comb can be determined with a relative accuracy of 10 . One of the comb frequencies coincides with the 6 x 10" th multiple of the caesium clock frequency. How accurate can the frequency of a molecular transition at A = 750 nm be measured ... 

The best frequency stability in the optical range can be achieved with the optical frequency-comb technique, which will be discussed in Vol. 2, Sect. 9.7 [377]. The relative frequency fluctuations go down to Av/uq < 10 , which implies an absolute stability of about 0.5 Hz. 

This positive development is partly based on new experimental techniques, such as improvements of existing lasers and the invention of new laser types, the realization of optical parametric oscillators and amplifiers in the femtosecond range, the generation of attosecond pulses, the revolution in the measurements of absolute optical frequencies and phases of optical waves using the optical frequency comb, or the different methods developed for the generation of Bose-Einstein condensates of atoms and molecules and the demonstration of atom lasers as a particle equivalent to photon lasers. 

M. Kourogi, B. Widiyatomoko, Y. Ihkeuchi, M. Ohtsu Limit of optical-frequency comb generation due to material dispersion. IEEE J. Quantum Electron. QE-31, 2120 (1995)... 

S.A. Diddams, L.S. Ma, J. Ye, J.L. Hall Broadband optical frequency comb generation with a phase-modulated parametric oscillator. Opt. Lett. 24, 1747 (1999)... 

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